One of the major advantages of the present model is that, for states without longitudinal excitation, e.g. \(\pi \) , \(\rho \) , \(K\) , which are those attracting most of the attention, the predicted masses and wave functions are very close to the predictions of LFH. Thus, leading phenomenological successes of LFH remain intact in the present approach (cf. [1]}). Exceptions may arise for observables sensitive to the endpoints. One notable example is the elastic form factor, \(F_\pi (Q^2) = \int _0^1{\mathrm {d}}x \chi ^2(x) \exp \big [-((1-x){Q^2})/(4x\kappa ^2)\big ]\) . At small \(Q^2\) , the pion form factor obtained from our work is close to that from LFH with IMA. However, at large \(Q^2\) , form factor from LFH with IMA scales as \(Q^2F_\pi (Q^2) \rightarrow \exp (-c Q^2)\) , whereas from our model \(Q^2F_\pi (Q^2) \rightarrow 1/(Q^2)^\mu \sim 1/\ln Q^2\)  since \(\mu =2m_{u,d}/\sigma \ll 1\) . Further work is needed to examine the connections of the longitudinal confinement with both the quark condensate (cf. in-hadron condensate [2]}) as well as with the successful heavy quark effective theory. It will also be interesting to explore the formal link between the present model and the top-down holographic models, which would provide useful guidance for physics beyond the semiclassical approximation.
